The original renewal application represents continued research in corrective SPECT reconstruction for the 9th to 13th year. During the last decade, substantial progress has been made in Single-Photon Emission Computed Tomography (SPECT) both in terms of image quality and quantitative accuracy. Reconstruction methods with built-in correction for image degrading factors have played an important role in the advancement. This grant research has contributed significantly to the progress in the field as indicated by the publication record. In this renewal application, we propose to continue to pursue the broad, long- term objectives laid out in the previous application, i.e., to improve the image quality and quantitative accuracy of SPECT images through the development and implementation of image reconstruction methods that correct for various image degrading factors. In the present application, specific aims are proposed to extend the previous work and to explore new directions that will lead to new improvements rn SPECT. In specific aim #1, we propose to continue and extend development of fast, stable, and accurate non-iterative and iterative reconstruction algorithms that have fast convergence and good noise characteristics. We are particularly interested in truly fast iterative reconstruction algorithms that are suitable for clinical use. In specific aim #2, we propose to continue development of accurate, robust and efficient 3D and 4D compensation methods for imaging degrading factors. We will extend our work in exact modeling of the image degrading factors to include scatter in non-uniform scattering media and collimator penetration and scatter. Also, we will extend our work from three spatial dimensions to include a fourth time dimension. Fast implementations of the correction reconstruction methods will be developed for practical and clinical use. In specific aim #3, we will continue the development of a 3D mathematical cardiac-chest phantom and to extend it to include a realistic beating heart model. We will investigate the characteristics of corrective reconstruction methods including spatial resolution and noise. Also, we propose to evaluate the efficacy of the corrective reconstruction methods using phantom studies and comprehensive observer experiments. In specific aim #1, we propose to evaluate the potential applications of corrective reconstruction methods in several clinical areas. We propose a comprehensive evaluation of the clinical usefulness of corrective reconstruction methods in thallium myocardial perfusion SPECT. Also, we propose to initiate preliminary evaluation of clinical applications of corrective reconstruction methods for gated 4D cardiac SPECT, gallium SPECT in malignant lymphoma, and Tc-99m sestamibi SPECT in breast cancer.